The power to subpoena is available to an attorney or a pro se litigant once a case is underway. The Court does not need to sign a subpoena or otherwise approve it, but will get involved upon request only if the subpoenaed party fails to respond. The form on the court website is available for your use so that whoever you serve a subpoena on will understand what it is you are seeking. I do urge you to consult with a local attorney before you send out the subpoenas because document requests such as this are very technical and it may not be possible to get the documents in the time frame you have specified.
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In most instances, a subpoena can be issued and signed by an attorney on behalf of a court in which the attorney is authorized to practice law.
In a very limited few cases, a non-lawyer may issue a subpoena if acting on his or her own behalf and in many others a non lawyer using subpoena power is tantamount to the illegal practice of alw and can be sanctioned.
Find out BEFORE rather than after if your state allows pro se subpoena power
And yes, you likely do need an attorney